<p><b>Abstract</b>—Fault-tolerant communication algorithms for <tmath>$k$</tmath>-ary <tmath>$n$</tmath>-cubes are introduced. These include: One-to-all broadcasting, all-to-all broadcasting, one-to-all personalized communication, and all-to-all personalized communication. Each of these algorithms can tolerate up to <tmath>$(2n-2)$</tmath> node failures provided that <tmath>$k > (2n-2)$</tmath> and <tmath>$k > 3$</tmath>. Extensions of these algorithms with up to <tmath>$2n-1$</tmath> node failures are also described. The communication complexities of the proposed algorithms are derived when wormhole or store and forward packet routing is used.</p>